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Answer: Interval and radius of convergence Determine the

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 11E Chapter 9.2

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 11E

Problem 11E

Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.

Step-by-Step Solution:

Solution 11E

Step 1:

Given series is and
To determine the radius of convergence we use ratio test which states:

The ratio test states that:
a. If  
then the series converges
b. If
then the series diverges
c. If
or the limit does not exist then the test is inconclusive.

Calculating L, we get

 

 


Since
and independent of x, we can conclude that the series converges for all x.

Thus the interval of convergence is the interval . The radius of convergence in this case is said to be  .

Step 2 of 1

Chapter 9.2, Problem 11E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Answer: Interval and radius of convergence Determine the